jika fx = x kurang 2 per x kuadrat + X kurang 6 dan GX = x kuadrat min 5 x + 6 per x kuadrat min 3 x + 2 maka limit x mendekati 2 integral FX * GX​

Jawaban:

Pembahasan

Jika f(x) = (x – 2)/(x² + x – 6) dan g(x) = (x² – 5x + 6)/(x² – 3x + 2)

Fungsi f(x) dan g(x) kita sederhanakan terlebih dahulu

f(x) = (x – 2)/(x² + x – 6)

f(x) = (x – 2)/(x – 2)(x + 3)

f(x) = 1/(x + 3)

.

g(x) = (x² – 5x + 6)/(x² – 3x + 2)

g(x) = (x – 2)(x – 3)/(x – 2)(x – 1)

g(x) = (x – 3)/(x – 1)

.

Maka:

lim x → 2 { f(x) . g(x) }

lim x → 2 { 1/(x + 3) . (x – 3)/(x – 1) }

Substitusi nilai x = 2

= { 1/(x + 3) . (x – 3)/(x – 1) }

= { 1/(2 + 3) . (2 – 3)/(2 – 1) }

= { 1/5 . (-1)/(1) }

= { 1/5 . (-1) }

= -1/5

Opsi { C }